Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincare invariance

The fulfillment of the space-asymptotic Poincare algebra is used to derive new higher-order-in-spin interaction Hamiltonians for binary black holes in the Arnowitt-Deser-Misner canonical formalism almost completing the set of the formally 1/c(4) spin-interaction Hamiltonians involving nonlinear spin terms. To linear order in G, the expressions for the S(3)p and the S(2)p(2) Hamiltonians are completed. It is also shown that there are no quartic nonlinear S-4 Hamiltonians to linear order in G.